NPB Model for Birth Weight
Sheena Martenies
02/10/2021
#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------
#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.0.6 ✓ dplyr 1.0.4
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(haven)
library(readxl)
library(mmpack)
#' For ggplots
simple_theme <- theme(
#aspect.ratio = 1,
text = element_text(family="Calibri",size = 12, color = 'black'),
panel.spacing.y = unit(0,"cm"),
panel.spacing.x = unit(0.25, "lines"),
panel.grid.minor = element_line(color = "transparent"),
panel.grid.major = element_line(color = "transparent"),
panel.border=element_rect(fill = NA),
panel.background=element_blank(),
axis.ticks = element_line(colour = "black"),
axis.text = element_text(color = "black", size=10),
# legend.position = c(0.1,0.1),
plot.margin=grid::unit(c(0,0,0,0), "mm"),
legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation
set.seed(123)1 Sensitivty Analysis
In this version of the analysis, we are stratifying by race/ethnicity. This is the script for non-NHW participants. 05_NPB_Model_BW_v4b.Rmd has the script for all NHW participants
1.1 Exposure data
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072 51.81487 6.006276 43.30893
## [2,] 6.598608 50.05090 58.32885 7.281109 48.36432
## [3,] 7.122537 50.14275 59.28421 3.357792 28.16745
## [4,] 7.637453 47.03125 55.32825 10.743612 45.87564
## [5,] 7.132364 48.46291 57.52274 5.166432 59.10860
## [6,] 7.245673 48.97393 56.14186 5.191274 26.88517
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] 10128.4962 2827.538 729.2371 4829.780
## [2,] 10749.0359 1576.420 5239.2211 4417.792
## [3,] 858.7283 2923.811 3427.2247 7006.042
## [4,] 15603.9800 3364.200 3166.5395 4484.960
## [5,] 4889.8576 2455.659 6164.1160 2206.505
## [6,] 2558.2207 3767.916 5762.0471 5376.856
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] 7968.654 29116.58 1749.1256 275.2480 155.7767
## [2,] 3780.951 51044.30 7354.5310 279.6435 226.8038
## [3,] 6806.912 29145.98 729.7784 194.1983 101.0046
## [4,] 5265.285 43921.85 5870.6867 174.3361 120.3281
## [5,] 11764.143 35210.72 3554.4858 293.6834 201.4526
## [6,] 6123.707 40422.63 5254.6965 286.1329 199.0948
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 14.377133 37.32935 31.784946 11.529628
## [2,] 8.905404 67.03932 15.290231 4.908306
## [3,] 5.435988 22.49834 12.919186 5.234103
## [4,] 5.035971 47.15500 3.842365 10.000000
## [5,] 15.269587 55.92441 53.908629 27.461416
## [6,] 15.269587 55.92441 10.114247 8.240705
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 26.114650 12.010919 90.33703
## [2,] 8.500401 18.123496 30.44025
## [3,] 6.307385 2.115768 73.60772
## [4,] 5.121799 25.171768 23.08698
## [5,] 37.742207 49.368155 91.67060
## [6,] 1.983365 9.149072 48.58072Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 0.40878878 0.01378123 0.05028648 -0.09908112
## mean_o3 0.01378123 9.82940898 12.62787148 -0.29071188
## mean_temp 0.05028648 12.62787148 21.97189056 0.64211293
## pct_tree_cover -0.09908112 -0.29071188 0.64211293 5.31164400
## pct_impervious 0.65248434 -0.71842181 2.94316568 0.21810136
## mean_aadt_intensity -316.60274061 233.59559080 2237.86511575 4153.38447704
## dist_m_tri -283.75781768 107.78779938 -92.09652567 1157.03833690
## dist_m_npl -247.47893930 564.99435312 797.66623054 1651.13725267
## dist_m_waste_site -256.87856646 295.90720632 595.67129800 1474.01548662
## dist_m_major_emit 75.78034383 542.77236728 731.71425416 1210.35674672
## dist_m_cafo -796.78809693 113.64418517 1788.77467105 6740.82668034
## dist_m_mine_well -246.15307838 -174.02154821 347.43839722 1843.07939334
## cvd_rate_adj 2.75466082 -0.19042942 3.57768901 -10.49859007
## res_rate_adj 1.92445952 -2.36449701 4.04898468 0.69481473
## violent_crime_rate 0.10159573 0.81293604 0.85366032 -0.85575848
## property_crime_rate 0.25735425 1.67359388 6.68954912 -5.59386200
## pct_less_hs 1.20446927 -0.25462044 -0.57677069 -5.96024136
## pct_unemp 0.12334849 0.18674932 0.47458851 -0.57257461
## pct_limited_eng 0.43490226 -0.35212589 -0.34012225 -2.59639577
## pct_hh_pov 0.86532874 -0.07963960 1.31570281 -1.49233483
## pct_poc 1.51246448 0.06712855 -2.21652590 -14.48950230
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.6524843 -316.6027 -283.75782
## mean_o3 -0.7184218 233.5956 107.78780
## mean_temp 2.9431657 2237.8651 -92.09653
## pct_tree_cover 0.2181014 4153.3845 1157.03834
## pct_impervious 118.6040354 36640.1009 -7553.17944
## mean_aadt_intensity 36640.1009233 57641629.8679 1565979.88108
## dist_m_tri -7553.1794392 1565979.8811 4608012.31878
## dist_m_npl -729.1756706 5991441.6628 3514059.77440
## dist_m_waste_site -5336.7915482 2680197.5003 2541111.37856
## dist_m_major_emit 5112.3800727 5142469.5768 1039857.82892
## dist_m_cafo 7343.4578780 11401543.4858 5158574.42432
## dist_m_mine_well -1846.0608375 519042.2111 1347393.64163
## cvd_rate_adj 153.7257890 15475.7180 -40115.15023
## res_rate_adj 116.3216711 18162.7204 -24071.77748
## violent_crime_rate 14.9035752 5092.8427 -451.49611
## property_crime_rate 37.8897147 15294.9122 2942.56251
## pct_less_hs 54.1512649 -12322.2405 -14640.56309
## pct_unemp 26.7371633 4117.1570 -3067.22587
## pct_limited_eng 42.4716032 -4034.8173 -6400.69993
## pct_hh_pov 76.6828013 9296.3905 -8933.86683
## pct_poc 82.2532162 4907.0965 -20638.86724
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -247.4789 -256.8786 75.78034
## mean_o3 564.9944 295.9072 542.77237
## mean_temp 797.6662 595.6713 731.71425
## pct_tree_cover 1651.1373 1474.0155 1210.35675
## pct_impervious -729.1757 -5336.7915 5112.38007
## mean_aadt_intensity 5991441.6628 2680197.5003 5142469.57683
## dist_m_tri 3514059.7744 2541111.3786 1039857.82892
## dist_m_npl 9755104.6822 3957347.1872 5676625.89348
## dist_m_waste_site 3957347.1872 5491944.2186 485019.21046
## dist_m_major_emit 5676625.8935 485019.2105 8317441.29166
## dist_m_cafo 7442271.8989 5706643.6152 -433351.36369
## dist_m_mine_well 373875.1037 1208648.3948 -1461468.74425
## cvd_rate_adj -22672.7435 -49151.9480 18167.43502
## res_rate_adj -6928.6332 -36249.6167 4967.77652
## violent_crime_rate 122.5328 -2674.5446 1187.95371
## property_crime_rate 3440.5949 -9452.8830 -5663.16784
## pct_less_hs -15551.2855 -18040.7331 3187.36083
## pct_unemp 584.7544 -3365.1520 3672.57470
## pct_limited_eng -3639.5214 -8519.3551 7516.33514
## pct_hh_pov -2571.7777 -12025.9897 8216.38301
## pct_poc -14283.4119 -17498.2028 11624.47703
## dist_m_cafo dist_m_mine_well cvd_rate_adj
## mean_pm -796.7881 -246.1531 2.7546608
## mean_o3 113.6442 -174.0215 -0.1904294
## mean_temp 1788.7747 347.4384 3.5776890
## pct_tree_cover 6740.8267 1843.0794 -10.4985901
## pct_impervious 7343.4579 -1846.0608 153.7257890
## mean_aadt_intensity 11401543.4858 519042.2111 15475.7180391
## dist_m_tri 5158574.4243 1347393.6416 -40115.1502286
## dist_m_npl 7442271.8989 373875.1037 -22672.7434832
## dist_m_waste_site 5706643.6152 1208648.3948 -49151.9479803
## dist_m_major_emit -433351.3637 -1461468.7442 18167.4350205
## dist_m_cafo 33511609.3448 6740561.1503 -24023.6790132
## dist_m_mine_well 6740561.1503 3673789.1331 -29492.8084450
## cvd_rate_adj -24023.6790 -29492.8084 1568.8304090
## res_rate_adj 7304.5199 -9245.1715 1027.7940865
## violent_crime_rate 2046.3298 -1179.9052 100.9225559
## property_crime_rate 5869.2804 -254.6397 208.2848909
## pct_less_hs -28844.6823 -8405.9488 301.0825676
## pct_unemp -1540.9735 -2881.3500 97.0763049
## pct_limited_eng -10163.8795 -3977.1750 177.0027630
## pct_hh_pov -3195.2854 -4913.3159 262.6447410
## pct_poc -46671.0930 -22472.3318 481.1037946
## res_rate_adj violent_crime_rate property_crime_rate
## mean_pm 1.9244595 0.1015957 0.2573543
## mean_o3 -2.3644970 0.8129360 1.6735939
## mean_temp 4.0489847 0.8536603 6.6895491
## pct_tree_cover 0.6948147 -0.8557585 -5.5938620
## pct_impervious 116.3216711 14.9035752 37.8897147
## mean_aadt_intensity 18162.7203792 5092.8427356 15294.9121570
## dist_m_tri -24071.7774777 -451.4961084 2942.5625099
## dist_m_npl -6928.6332227 122.5327963 3440.5948584
## dist_m_waste_site -36249.6167432 -2674.5446453 -9452.8829545
## dist_m_major_emit 4967.7765250 1187.9537119 -5663.1678442
## dist_m_cafo 7304.5198783 2046.3297823 5869.2803721
## dist_m_mine_well -9245.1714629 -1179.9052006 -254.6397468
## cvd_rate_adj 1027.7940865 100.9225559 208.2848909
## res_rate_adj 940.1945728 76.9892329 240.8826506
## violent_crime_rate 76.9892329 25.5420603 71.9963533
## property_crime_rate 240.8826506 71.9963533 491.8000334
## pct_less_hs 185.5325753 20.6749023 22.5843969
## pct_unemp 69.2602680 10.6933742 18.5207079
## pct_limited_eng 99.1158417 11.2428807 1.1062078
## pct_hh_pov 204.6089131 27.8143880 65.8300381
## pct_poc 206.2218350 36.2845531 9.5271261
## pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## mean_pm 1.2044693 0.1233485 0.4349023 0.8653287
## mean_o3 -0.2546204 0.1867493 -0.3521259 -0.0796396
## mean_temp -0.5767707 0.4745885 -0.3401222 1.3157028
## pct_tree_cover -5.9602414 -0.5725746 -2.5963958 -1.4923348
## pct_impervious 54.1512649 26.7371633 42.4716032 76.6828013
## mean_aadt_intensity -12322.2404976 4117.1570121 -4034.8172805 9296.3904978
## dist_m_tri -14640.5630864 -3067.2258670 -6400.6999345 -8933.8668309
## dist_m_npl -15551.2854862 584.7543739 -3639.5214452 -2571.7776685
## dist_m_waste_site -18040.7330880 -3365.1520125 -8519.3551489 -12025.9896947
## dist_m_major_emit 3187.3608343 3672.5746989 7516.3351376 8216.3830073
## dist_m_cafo -28844.6823465 -1540.9735482 -10163.8795343 -3195.2853551
## dist_m_mine_well -8405.9488274 -2881.3500245 -3977.1749583 -4913.3158874
## cvd_rate_adj 301.0825676 97.0763049 177.0027630 262.6447410
## res_rate_adj 185.5325753 69.2602680 99.1158417 204.6089131
## violent_crime_rate 20.6749023 10.6933742 11.2428807 27.8143880
## property_crime_rate 22.5843969 18.5207079 1.1062078 65.8300381
## pct_less_hs 176.2436488 36.8702016 94.5119085 114.6493750
## pct_unemp 36.8702016 25.9815492 24.8257135 39.4311861
## pct_limited_eng 94.5119085 24.8257135 82.1564459 78.3635031
## pct_hh_pov 114.6493750 39.4311861 78.3635031 139.7618779
## pct_poc 211.2594439 55.4382200 130.3042297 144.6790148
## pct_poc
## mean_pm 1.51246448
## mean_o3 0.06712855
## mean_temp -2.21652590
## pct_tree_cover -14.48950230
## pct_impervious 82.25321621
## mean_aadt_intensity 4907.09649773
## dist_m_tri -20638.86723571
## dist_m_npl -14283.41186439
## dist_m_waste_site -17498.20282580
## dist_m_major_emit 11624.47703351
## dist_m_cafo -46671.09304576
## dist_m_mine_well -22472.33183580
## cvd_rate_adj 481.10379457
## res_rate_adj 206.22183502
## violent_crime_rate 36.28455311
## property_crime_rate 9.52712614
## pct_less_hs 211.25944392
## pct_unemp 55.43822005
## pct_limited_eng 130.30422969
## pct_hh_pov 144.67901481
## pct_poc 409.88652102ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 1.5833180 -0.2917235 -0.1814489 -0.04443914 0.03879239
## [2,] -1.3640362 0.6205574 1.2082246 0.50870576 0.50299234
## [3,] -0.5445851 0.6498540 1.4120376 -1.19360531 -1.35153943
## [4,] 0.2607677 -0.3425882 0.5680847 2.01107115 0.27447500
## [5,] -0.5292159 0.1140521 1.0362516 -0.40884423 1.48956214
## [6,] -0.3519956 0.2770483 0.7416578 -0.39806522 -1.46928234
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] -0.09314684 -0.39604630 -1.67331945 -0.21569109
## [2,] -0.01141308 -0.97887591 -0.22934656 -0.39149218
## [3,] -1.31410486 -0.35119772 -0.80949801 0.71295064
## [4,] 0.62805092 -0.14604407 -0.89296224 -0.36283056
## [5,] -0.78314878 -0.56928493 0.06677935 -1.33507945
## [6,] -1.09025795 0.04202559 -0.06195205 0.01775393
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] -0.4009504 -1.2930817 -0.6604666 0.4677498 -0.5230745
## [2,] -1.8529984 2.4947942 2.2640219 0.5787233 1.7933345
## [3,] -0.8037737 -1.2880039 -1.1922870 -1.5785230 -2.3093604
## [4,] -1.3383191 1.2644356 1.4898610 -2.0799847 -1.6791619
## [5,] 0.9151010 -0.2403563 0.2814377 0.9331902 0.9665552
## [6,] -1.0406688 0.6599675 1.1684827 0.7425635 0.8896573
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 0.1461888 -0.6678858 0.7904517 0.01287583
## [2,] -0.9364825 0.6718153 -0.4520245 -1.28613316
## [3,] -1.6229633 -1.3366556 -0.6306252 -1.22221641
## [4,] -1.7021132 -0.2248212 -1.3143432 -0.28721538
## [5,] 0.3227753 0.1706146 2.4569339 3.13846569
## [6,] 0.3227753 0.1706146 -0.8419092 -0.63236396
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 1.6287966 -0.56661655 1.2779789
## [2,] -0.3145189 -0.04956957 -1.6805216
## [3,] -0.5564662 -1.40362153 0.4516629
## [4,] -0.6872676 0.54662531 -2.0437238
## [5,] 2.9116224 2.59333462 1.3438483
## [6,] -1.0335195 -0.80869270 -0.7845040Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 1.000000000 0.006875034 0.016779077 -0.067239882
## mean_o3 0.006875034 1.000000000 0.859276109 -0.040233202
## mean_temp 0.016779077 0.859276109 1.000000000 0.059437868
## pct_tree_cover -0.067239882 -0.040233202 0.059437868 1.000000000
## pct_impervious 0.093706751 -0.021040985 0.057654242 0.008689487
## mean_aadt_intensity -0.065222443 0.009813701 0.062882828 0.237366556
## dist_m_tri -0.206748105 0.016015817 -0.009152774 0.233871044
## dist_m_npl -0.123928958 0.057698489 0.054484319 0.229378511
## dist_m_waste_site -0.171441252 0.040274372 0.054226291 0.272913179
## dist_m_major_emit 0.041097198 0.060028730 0.054126872 0.182097525
## dist_m_cafo -0.215276049 0.006261608 0.065921075 0.505243853
## dist_m_mine_well -0.200862414 -0.028958910 0.038671141 0.417227044
## cvd_rate_adj 0.108775391 -0.001533495 0.019269963 -0.115008119
## res_rate_adj 0.098163589 -0.024596097 0.028171083 0.009832086
## violent_crime_rate 0.031441121 0.051305593 0.036034908 -0.073469785
## property_crime_rate 0.018150458 0.024070887 0.064353009 -0.109446781
## pct_less_hs 0.141902323 -0.006117484 -0.009268570 -0.194801649
## pct_unemp 0.037848775 0.011685917 0.019863281 -0.048739950
## pct_limited_eng 0.075044931 -0.012391202 -0.008005353 -0.124289829
## pct_hh_pov 0.114482020 -0.002148676 0.023742679 -0.054771853
## pct_poc 0.116843319 0.001057576 -0.023356474 -0.310532579
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.093706751 -0.065222443 -0.206748105
## mean_o3 -0.021040985 0.009813701 0.016015817
## mean_temp 0.057654242 0.062882828 -0.009152774
## pct_tree_cover 0.008689487 0.237366556 0.233871044
## pct_impervious 1.000000000 0.443137805 -0.323089805
## mean_aadt_intensity 0.443137805 1.000000000 0.096086248
## dist_m_tri -0.323089805 0.096086248 1.000000000
## dist_m_npl -0.021437122 0.252666254 0.524126794
## dist_m_waste_site -0.209106459 0.150638372 0.505130772
## dist_m_major_emit 0.162771561 0.234859825 0.167966347
## dist_m_cafo 0.116480502 0.259416670 0.415121515
## dist_m_mine_well -0.088438051 0.035667892 0.327476821
## cvd_rate_adj 0.356376451 0.051462951 -0.471806161
## res_rate_adj 0.348338943 0.078019633 -0.365714748
## violent_crime_rate 0.270777620 0.132728497 -0.041616853
## property_crime_rate 0.156883520 0.090841560 0.061812257
## pct_less_hs 0.374543388 -0.122254490 -0.513741000
## pct_unemp 0.481651675 0.106389013 -0.280321508
## pct_limited_eng 0.430257154 -0.058632029 -0.328965104
## pct_hh_pov 0.595598881 0.103574267 -0.352036987
## pct_poc 0.373053688 0.031924540 -0.474894591
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -0.123928958 -0.17144125 0.04109720
## mean_o3 0.057698489 0.04027437 0.06002873
## mean_temp 0.054484319 0.05422629 0.05412687
## pct_tree_cover 0.229378511 0.27291318 0.18209753
## pct_impervious -0.021437122 -0.20910646 0.16277156
## mean_aadt_intensity 0.252666254 0.15063837 0.23485982
## dist_m_tri 0.524126794 0.50513077 0.16796635
## dist_m_npl 1.000000000 0.54066111 0.63020150
## dist_m_waste_site 0.540661105 1.00000000 0.07176307
## dist_m_major_emit 0.630201503 0.07176307 1.00000000
## dist_m_cafo 0.411615692 0.42064918 -0.02595659
## dist_m_mine_well 0.062453023 0.26907900 -0.26438545
## cvd_rate_adj -0.183273683 -0.52952891 0.15904160
## res_rate_adj -0.072347368 -0.50446552 0.05617697
## violent_crime_rate 0.007762622 -0.22581814 0.08150358
## property_crime_rate 0.049673332 -0.18188921 -0.08854627
## pct_less_hs -0.375053817 -0.57987500 0.08324911
## pct_unemp 0.036730344 -0.28171444 0.24982923
## pct_limited_eng -0.128560483 -0.40107246 0.28753482
## pct_hh_pov -0.069650316 -0.43407363 0.24098579
## pct_poc -0.225883326 -0.36880650 0.19908876
## dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.215276049 -0.200862414 0.108775391 0.098163589
## mean_o3 0.006261608 -0.028958910 -0.001533495 -0.024596097
## mean_temp 0.065921075 0.038671141 0.019269963 0.028171083
## pct_tree_cover 0.505243853 0.417227044 -0.115008119 0.009832086
## pct_impervious 0.116480502 -0.088438051 0.356376451 0.348338943
## mean_aadt_intensity 0.259416670 0.035667892 0.051462951 0.078019633
## dist_m_tri 0.415121515 0.327476821 -0.471806161 -0.365714748
## dist_m_npl 0.411615692 0.062453023 -0.183273683 -0.072347368
## dist_m_waste_site 0.420649183 0.269079002 -0.529528911 -0.504465523
## dist_m_major_emit -0.025956591 -0.264385448 0.159041603 0.056176970
## dist_m_cafo 1.000000000 0.607493028 -0.104774085 0.041151452
## dist_m_mine_well 0.607493028 1.000000000 -0.388482105 -0.157307340
## cvd_rate_adj -0.104774085 -0.388482105 1.000000000 0.846270584
## res_rate_adj 0.041151452 -0.157307340 0.846270584 1.000000000
## violent_crime_rate 0.069943928 -0.121804137 0.504164518 0.496813238
## property_crime_rate 0.045718601 -0.005990662 0.237123988 0.354243895
## pct_less_hs -0.375328359 -0.330348920 0.572586196 0.455779267
## pct_unemp -0.052223385 -0.294921467 0.480831284 0.443141860
## pct_limited_eng -0.193705095 -0.228926866 0.493027592 0.356626311
## pct_hh_pov -0.046689330 -0.216831917 0.560901170 0.564444590
## pct_poc -0.398215822 -0.579107525 0.599955397 0.332195663
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.031441121 0.018150458 0.141902323
## mean_o3 0.051305593 0.024070887 -0.006117484
## mean_temp 0.036034908 0.064353009 -0.009268570
## pct_tree_cover -0.073469785 -0.109446781 -0.194801649
## pct_impervious 0.270777620 0.156883520 0.374543388
## mean_aadt_intensity 0.132728497 0.090841560 -0.122254490
## dist_m_tri -0.041616853 0.061812257 -0.513741000
## dist_m_npl 0.007762622 0.049673332 -0.375053817
## dist_m_waste_site -0.225818142 -0.181889213 -0.579874999
## dist_m_major_emit 0.081503580 -0.088546273 0.083249114
## dist_m_cafo 0.069943928 0.045718601 -0.375328359
## dist_m_mine_well -0.121804137 -0.005990662 -0.330348920
## cvd_rate_adj 0.504164518 0.237123988 0.572586196
## res_rate_adj 0.496813238 0.354243895 0.455779267
## violent_crime_rate 1.000000000 0.642374450 0.308147582
## property_crime_rate 0.642374450 1.000000000 0.076710972
## pct_less_hs 0.308147582 0.076710972 1.000000000
## pct_unemp 0.415101478 0.163844091 0.544861664
## pct_limited_eng 0.245430660 0.005503280 0.785432692
## pct_hh_pov 0.465529473 0.251093497 0.730500622
## pct_poc 0.354618997 0.021219533 0.786009104
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.03784877 0.075044931 0.114482020 0.116843319
## mean_o3 0.01168592 -0.012391202 -0.002148676 0.001057576
## mean_temp 0.01986328 -0.008005353 0.023742679 -0.023356474
## pct_tree_cover -0.04873995 -0.124289829 -0.054771853 -0.310532579
## pct_impervious 0.48165167 0.430257154 0.595598881 0.373053688
## mean_aadt_intensity 0.10638901 -0.058632029 0.103574267 0.031924540
## dist_m_tri -0.28032151 -0.328965104 -0.352036987 -0.474894591
## dist_m_npl 0.03673034 -0.128560483 -0.069650316 -0.225883326
## dist_m_waste_site -0.28171444 -0.401072461 -0.434073632 -0.368806502
## dist_m_major_emit 0.24982923 0.287534819 0.240985793 0.199088756
## dist_m_cafo -0.05222339 -0.193705095 -0.046689330 -0.398215822
## dist_m_mine_well -0.29492147 -0.228926866 -0.216831917 -0.579107525
## cvd_rate_adj 0.48083128 0.493027592 0.560901170 0.599955397
## res_rate_adj 0.44314186 0.356626311 0.564444590 0.332195663
## violent_crime_rate 0.41510148 0.245430660 0.465529473 0.354618997
## property_crime_rate 0.16384409 0.005503280 0.251093497 0.021219533
## pct_less_hs 0.54486166 0.785432692 0.730500622 0.786009104
## pct_unemp 1.00000000 0.537339041 0.654354292 0.537211051
## pct_limited_eng 0.53733904 1.000000000 0.731305192 0.710077699
## pct_hh_pov 0.65435429 0.731305192 1.000000000 0.604476415
## pct_poc 0.53721105 0.710077699 0.604476415 1.000000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.2 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
W <- select(hs_data2,
lat, lon, lat_lon_int,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w) %>%
as.matrix()
head(W)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.79402 -104.8133 -4170.944 0 0 1 0 0
## [2,] 39.62671 -104.9927 -4160.517 0 0 1 0 0
## [3,] 39.79134 -104.7669 -4168.814 0 0 0 1 0
## [4,] 39.68050 -104.9451 -4164.274 0 0 1 0 0
## [5,] 39.74073 -104.8516 -4166.881 1 0 0 0 0
## [6,] 39.69147 -104.7602 -4158.086 0 1 0 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1
## [3,] 0 0 1 0 0 1
## [4,] 0 0 0 0 0 1
## [5,] 1 0 1 0 0 1
## [6,] 0 1 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 19 0 1
## [2,] 0 0 0 36 0 0
## [3,] 0 0 0 30 0 0
## [4,] 0 0 0 22 0 0
## [5,] 0 0 0 32 0 1
## [6,] 0 0 0 27 0 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 29 0 0 40.57143
## [2,] 19 2 1 35.85714
## [3,] 15 0 1 38.42857
## [4,] 17 1 0 40.71429
## [5,] 18 0 0 40.28571
## [6,] 17 7 0 40.00000Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:17], W.s[,4],
W[,19:20], W.s[,5:6],
W[,23], W.s[,7])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "" ""colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 1.1167843 0.51514286 -0.7374184 0 0 1 0 0
## [2,] -1.8516422 -2.09256135 0.7445400 0 0 1 0 0
## [3,] 1.0692021 1.19072454 -0.4346320 0 0 0 1 0
## [4,] -0.8972660 -1.40025129 0.2104678 0 0 1 0 0
## [5,] 0.1713509 -0.04176901 -0.1600238 1 0 0 0 0
## [6,] -0.7026663 1.28759109 1.0899619 0 1 0 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1
## [3,] 0 0 1 0 0 1
## [4,] 0 0 0 0 0 1
## [5,] 1 0 1 0 0 1
## [6,] 0 1 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 -0.9872932 0 1
## [2,] 0 0 0 1.7854996 0 0
## [3,] 0 0 0 0.8068668 0 0
## [4,] 0 0 0 -0.4979769 0 0
## [5,] 0 0 0 1.1330778 0 1
## [6,] 0 0 0 0.3175505 0 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 2.95983287 -1.3146057 0 0.7383142
## [2,] 0.17922225 -0.7742175 1 -1.5631894
## [3,] -0.93302200 -1.3146057 1 -0.3078238
## [4,] -0.37689988 -1.0444116 0 0.8080568
## [5,] -0.09883881 -1.3146057 0 0.5988292
## [6,] -0.37689988 0.5767527 0 0.4593441summary(W.scaled)## lat lon lat_lon_int ed_no_hs
## Min. :-2.713877 Min. :-2.9703 Min. :-3.84454 Min. :0.00
## 1st Qu.:-0.641686 1st Qu.:-0.3049 1st Qu.:-0.39665 1st Qu.:0.00
## Median :-0.004541 Median : 0.1978 Median : 0.03426 Median :0.00
## Mean : 0.000000 Mean : 0.0000 Mean : 0.00000 Mean :0.25
## 3rd Qu.: 0.513104 3rd Qu.: 0.5538 3rd Qu.: 0.61126 3rd Qu.:0.25
## Max. : 4.719081 Max. : 2.1774 Max. : 2.93499 Max. :1.00
## ed_hs ed_aa ed_4yr low_bmi
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2854 Mean :0.3009 Mean :0.1084 Mean :0.0354
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## ovwt_bmi obese_bmi concep_spring concep_summer
## Min. :0.000 Min. :0.0000 Min. :0.00 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.00 1st Qu.:0.000
## Median :0.000 Median :0.0000 Median :0.00 Median :0.000
## Mean :0.292 Mean :0.2588 Mean :0.25 Mean :0.219
## 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:0.25 3rd Qu.:0.000
## Max. :1.000 Max. :1.0000 Max. :1.00 Max. :1.000
## concep_fall concep_2010 concep_2011 concep_2012
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2832 Mean :0.1659 Mean :0.3164 Mean :0.2898
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_2013 maternal_age any_smoker smokeSH
## Min. :0.0000 Min. :-1.4766 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:-0.8242 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.0000 Median :-0.1718 Median :0.000 Median :0.0000
## Mean :0.2257 Mean : 0.0000 Mean :0.104 Mean :0.3319
## 3rd Qu.:0.0000 3rd Qu.: 0.8069 3rd Qu.:0.000 3rd Qu.:1.0000
## Max. :1.0000 Max. : 2.9272 Max. :1.000 Max. :1.0000
## mean_cpss mean_epsd male gest_age_w
## Min. :-5.10394 Min. :-1.3146 Min. :0.0000 Min. :-6.6544
## 1st Qu.:-0.52752 1st Qu.:-0.7742 1st Qu.:0.0000 1st Qu.:-0.3078
## Median : 0.01702 Median :-0.1438 Median :1.0000 Median : 0.1804
## Mean : 0.00000 Mean : 0.0000 Mean :0.5111 Mean : 0.0000
## 3rd Qu.: 0.54997 3rd Qu.: 0.5768 3rd Qu.:1.0000 3rd Qu.: 0.5988
## Max. : 4.07208 Max. : 5.3051 Max. :1.0000 Max. : 2.6911Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int ed_no_hs
## lat 1.0000000000 -0.2197126628 -0.925354901 0.023704345
## lon -0.2197126628 1.0000000000 0.573149965 -0.020706192
## lat_lon_int -0.9253549015 0.5731499653 1.000000000 -0.027956367
## ed_no_hs 0.0237043446 -0.0207061919 -0.027956367 0.187915743
## ed_hs -0.0118544823 0.0341795076 0.023258551 -0.071507761
## ed_aa 0.0074435062 -0.0103199888 -0.010249527 -0.075388027
## ed_4yr -0.0110564389 0.0208198361 0.017353352 -0.027161863
## low_bmi -0.0001880928 -0.0056988431 -0.002050855 -0.006651885
## ovwt_bmi 0.0248936444 0.0136211023 -0.015634135 0.011086475
## obese_bmi 0.0107122204 -0.0280748233 -0.019899866 -0.004988914
## concep_spring -0.0223303960 0.0011338637 0.019209169 -0.007206208
## concep_summer 0.0203779870 -0.0366082745 -0.031356869 0.002771619
## concep_fall 0.0058156155 0.0376700058 0.009742659 0.019955654
## concep_2010 0.0219575397 0.0233177984 -0.009385304 -0.006097561
## concep_2011 0.0063177657 -0.0094195638 -0.008977235 0.018292683
## concep_2012 0.0156618197 0.0002195065 -0.013078318 -0.008314856
## concep_2013 -0.0464133651 -0.0152599647 0.033075931 -0.003325942
## maternal_age -0.0302790950 -0.0162109126 0.019088658 -0.119345460
## any_smoker -0.0054630028 0.0080912190 0.007738581 0.009423503
## smokeSH 0.0283665743 0.0097078774 -0.020047891 0.012195122
## mean_cpss -0.0247080882 0.0477415558 0.039275067 -0.067717014
## mean_epsd -0.0326272603 0.0794941258 0.058301007 0.050748754
## male 0.0320040663 -0.0174533275 -0.033655475 -0.023835920
## gest_age_w 0.0428155858 -0.0443601833 -0.053216199 0.011327363
## ed_hs ed_aa ed_4yr low_bmi
## lat -0.0118544823 0.0074435062 -0.0110564389 -0.0001880928
## lon 0.0341795076 -0.0103199888 0.0208198361 -0.0056988431
## lat_lon_int 0.0232585506 -0.0102495267 0.0173533517 -0.0020508553
## ed_no_hs -0.0715077605 -0.0753880266 -0.0271618625 -0.0066518847
## ed_hs 0.2043982890 -0.0860624375 -0.0310077900 -0.0056904028
## ed_aa -0.0860624375 0.2108196142 -0.0326903832 0.0137158331
## ed_4yr -0.0310077900 -0.0326903832 0.0968692973 -0.0016286325
## low_bmi -0.0056904028 0.0137158331 -0.0016286325 0.0342209054
## ovwt_bmi -0.0125777525 0.0050624963 0.0037478170 -0.0103604576
## obese_bmi 0.0168700822 0.0017659871 0.0007014893 -0.0091831329
## concep_spring 0.0083148559 0.0110864745 -0.0116407982 -0.0022172949
## concep_summer -0.0005641348 -0.0106155446 0.0028108628 0.0055334262
## concep_fall -0.0033946196 -0.0166591449 0.0047092989 -0.0033946196
## concep_2010 -0.0008977101 0.0009614819 0.0085797539 0.0007652611
## concep_2011 -0.0106695053 0.0021584287 -0.0055481428 0.0065145301
## concep_2012 0.0124453035 -0.0031395326 -0.0048809921 -0.0036300846
## concep_2013 -0.0002452760 -0.0015305221 0.0020897514 -0.0035712183
## maternal_age -0.0708295621 0.0194492453 0.1014068354 -0.0173049316
## any_smoker -0.0097865118 0.0174244059 -0.0112974118 0.0051802288
## smokeSH 0.0092910543 0.0174440280 -0.0271863901 0.0037478170
## mean_cpss -0.0170704310 0.0482904416 0.0212189132 0.0092354197
## mean_epsd -0.0009814900 0.0001820274 -0.0280010721 0.0143704449
## male 0.0023791771 0.0166199007 0.0065586798 -0.0048270314
## gest_age_w 0.0064377356 -0.0428762705 0.0228446044 -0.0133948146
## ovwt_bmi obese_bmi concep_spring concep_summer
## lat 0.024893644 0.0107122204 -0.022330396 0.0203779870
## lon 0.013621102 -0.0280748233 0.001133864 -0.0366082745
## lat_lon_int -0.015634135 -0.0198998660 0.019209169 -0.0313568686
## ed_no_hs 0.011086475 -0.0049889135 -0.007206208 0.0027716186
## ed_hs -0.012577752 0.0168700822 0.008314856 -0.0005641348
## ed_aa 0.005062496 0.0017659871 0.011086475 -0.0106155446
## ed_4yr 0.003747817 0.0007014893 -0.011640798 0.0028108628
## low_bmi -0.010360458 -0.0091831329 -0.002217295 0.0055334262
## ovwt_bmi 0.207209152 -0.0757608461 0.004434590 -0.0131075486
## obese_bmi -0.075760846 0.1922718443 -0.018292683 -0.0058228519
## concep_spring 0.004434590 -0.0182926829 0.187915743 -0.0548780488
## concep_summer -0.013107549 -0.0058228519 -0.054878049 0.1714331966
## concep_fall 0.005808135 0.0085748484 -0.070953437 -0.0621627455
## concep_2010 -0.008653337 -0.0009173322 -0.023835920 0.0101397092
## concep_2011 0.013833566 -0.0111208131 0.007206208 -0.0095804800
## concep_2012 -0.002786335 0.0157221906 -0.010532151 -0.0126219022
## concep_2013 -0.001746365 -0.0031100995 0.027716186 0.0125483194
## maternal_age 0.013377957 0.0577876541 -0.020975869 0.0017154510
## any_smoker -0.006043600 -0.0048025038 0.002771619 0.0037821557
## smokeSH -0.019523968 -0.0040519593 0.003325942 -0.0085454153
## mean_cpss -0.020707855 -0.0033427927 0.019318359 0.0132411329
## mean_epsd -0.020709593 0.0110314349 0.005616562 -0.0174792697
## male 0.005631537 0.0026735082 -0.019401330 -0.0124060593
## gest_age_w 0.024184017 -0.0142894672 -0.017280994 0.0199550304
## concep_fall concep_2010 concep_2011 concep_2012
## lat 0.0058156155 0.0219575397 0.006317766 0.0156618197
## lon 0.0376700058 0.0233177984 -0.009419564 0.0002195065
## lat_lon_int 0.0097426586 -0.0093853043 -0.008977235 -0.0130783182
## ed_no_hs 0.0199556541 -0.0060975610 0.018292683 -0.0083148559
## ed_hs -0.0033946196 -0.0008977101 -0.010669505 0.0124453035
## ed_aa -0.0166591449 0.0009614819 0.002158429 -0.0031395326
## ed_4yr 0.0047092989 0.0085797539 -0.005548143 -0.0048809921
## low_bmi -0.0033946196 0.0007652611 0.006514530 -0.0036300846
## ovwt_bmi 0.0058081353 -0.0086533367 0.013833566 -0.0027863352
## obese_bmi 0.0085748484 -0.0009173322 -0.011120813 0.0157221906
## concep_spring -0.0709534368 -0.0238359202 0.007206208 -0.0105321508
## concep_summer -0.0621627455 0.0101397092 -0.009580480 -0.0126219022
## concep_fall 0.2034417126 0.0216431529 -0.012185311 0.0108706316
## concep_2010 0.0216431529 0.1387035693 -0.052611699 -0.0481967310
## concep_2011 -0.0121853109 -0.0526116987 0.216760199 -0.0918951004
## concep_2012 0.0108706316 -0.0481967310 -0.091895100 0.2062820085
## concep_2013 -0.0197005671 -0.0375272256 -0.071551910 -0.0655475541
## maternal_age -0.0125842410 -0.0133747567 -0.049399227 0.0459459217
## any_smoker -0.0006867728 -0.0017708926 0.020245080 -0.0124649255
## smokeSH -0.0054941821 0.0024625709 0.018945117 -0.0232227302
## mean_cpss 0.0093518172 0.0092526974 -0.021988228 -0.0088771334
## mean_epsd 0.0496616702 -0.0299985136 0.031899640 -0.0137008756
## male 0.0123815317 0.0103555521 0.002035791 0.0089820066
## gest_age_w 0.0068109922 0.0120574543 -0.029097251 -0.0198243392
## concep_2013 maternal_age any_smoker smokeSH
## lat -0.0464133651 -0.030279095 -0.0054630028 0.0283665743
## lon -0.0152599647 -0.016210913 0.0080912190 0.0097078774
## lat_lon_int 0.0330759314 0.019088658 0.0077385809 -0.0200478908
## ed_no_hs -0.0033259424 -0.119345460 0.0094235033 0.0121951220
## ed_hs -0.0002452760 -0.070829562 -0.0097865118 0.0092910543
## ed_aa -0.0015305221 0.019449245 0.0174244059 0.0174440280
## ed_4yr 0.0020897514 0.101406835 -0.0112974118 -0.0271863901
## low_bmi -0.0035712183 -0.017304932 0.0051802288 0.0037478170
## ovwt_bmi -0.0017463650 0.013377957 -0.0060436003 -0.0195239684
## obese_bmi -0.0031100995 0.057787654 -0.0048025038 -0.0040519593
## concep_spring 0.0277161863 -0.020975869 0.0027716186 0.0033259424
## concep_summer 0.0125483194 0.001715451 0.0037821557 -0.0085454153
## concep_fall -0.0197005671 -0.012584241 -0.0006867728 -0.0054941821
## concep_2010 -0.0375272256 -0.013374757 -0.0017708926 0.0024625709
## concep_2011 -0.0715519102 -0.049399227 0.0202450798 0.0189451170
## concep_2012 -0.0655475541 0.045945922 -0.0124649255 -0.0232227302
## concep_2013 0.1751270530 0.019017182 -0.0057787022 0.0003335753
## maternal_age 0.0190171821 1.000000000 -0.0265798885 -0.1236724928
## any_smoker -0.0057787022 -0.026579889 0.0933765673 0.0496732924
## smokeSH 0.0003335753 -0.123672493 0.0496732924 0.2222200420
## mean_cpss 0.0150498420 0.047512237 0.0270005987 0.0695757378
## mean_epsd 0.0147146181 -0.090511822 0.0336448052 0.0944708964
## male -0.0202401742 0.058130104 -0.0066960344 -0.0014618449
## gest_age_w 0.0352270759 0.048984057 -0.0152234640 -0.0504214595
## mean_cpss mean_epsd male gest_age_w
## lat -0.024708088 -0.0326272603 0.032004066 0.042815586
## lon 0.047741556 0.0794941258 -0.017453327 -0.044360183
## lat_lon_int 0.039275067 0.0583010075 -0.033655475 -0.053216199
## ed_no_hs -0.067717014 0.0507487538 -0.023835920 0.011327363
## ed_hs -0.017070431 -0.0009814900 0.002379177 0.006437736
## ed_aa 0.048290442 0.0001820274 0.016619901 -0.042876270
## ed_4yr 0.021218913 -0.0280010721 0.006558680 0.022844604
## low_bmi 0.009235420 0.0143704449 -0.004827031 -0.013394815
## ovwt_bmi -0.020707855 -0.0207095934 0.005631537 0.024184017
## obese_bmi -0.003342793 0.0110314349 0.002673508 -0.014289467
## concep_spring 0.019318359 0.0056165615 -0.019401330 -0.017280994
## concep_summer 0.013241133 -0.0174792697 -0.012406059 0.019955030
## concep_fall 0.009351817 0.0496616702 0.012381532 0.006810992
## concep_2010 0.009252697 -0.0299985136 0.010355552 0.012057454
## concep_2011 -0.021988228 0.0318996396 0.002035791 -0.029097251
## concep_2012 -0.008877133 -0.0137008756 0.008982007 -0.019824339
## concep_2013 0.015049842 0.0147146181 -0.020240174 0.035227076
## maternal_age 0.047512237 -0.0905118217 0.058130104 0.048984057
## any_smoker 0.027000599 0.0336448052 -0.006696034 -0.015223464
## smokeSH 0.069575738 0.0944708964 -0.001461845 -0.050421459
## mean_cpss 1.000000000 0.4555278461 -0.014248699 -0.058556609
## mean_epsd 0.455527846 1.0000000000 0.007542429 -0.136977722
## male -0.014248699 0.0075424291 0.250431686 0.005788385
## gest_age_w -0.058556609 -0.1369777217 0.005788385 1.000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Response data: birth weight (in grams)
Y <- select(hs_data2, birth_weight) %>%
as.matrix()
head(Y)## birth_weight
## [1,] 2860
## [2,] 2755
## [3,] 3355
## [4,] 3810
## [5,] 2930
## [6,] 3235Distribution of birth weight and scaled birth weight
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
Dropping gest_age_w from the covariates
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"2 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 10000#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(bw_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 21 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(bw_ridge)## 22 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 3209.79864217149
## mean_pm -1.17201110995
## mean_o3 -0.96060373712
## mean_temp -0.57183600596
## pct_tree_cover 0.17202004715
## pct_impervious 0.01490879710
## mean_aadt_intensity 0.00010063296
## dist_m_tri 0.00012909382
## dist_m_npl 0.00014590679
## dist_m_waste_site 0.00031053298
## dist_m_major_emit 0.00036515555
## dist_m_cafo -0.00008288071
## dist_m_mine_well -0.00026813254
## cvd_rate_adj -0.03527224850
## res_rate_adj -0.03252749603
## violent_crime_rate -0.07375766433
## property_crime_rate 0.00637844214
## pct_less_hs 0.00093472723
## pct_unemp -0.41845995412
## pct_limited_eng -0.02741255114
## pct_hh_pov 0.00939489388
## pct_poc -0.04579457829Ridge regression predictions
ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0. Based on these results, it doesn’t look like there’s much here.
3 Nonparametric Bayesian Shrinkage (NPB): Birth weight
3.1 Finding the NPB priors
3.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.05695777 2.936959 0.00000 0.00000 0.012
## [2,] -2.24207523 14.551354 -35.68220 0.00000 0.040
## [3,] -0.60321006 6.334358 0.00000 0.00000 0.016
## [4,] 0.24631849 4.108479 0.00000 0.00000 0.008
## [5,] -0.01202969 1.647202 0.00000 0.00000 0.010
## [6,] 0.06117692 1.075446 0.00000 0.00000 0.004
## [7,] 0.40028362 3.413717 0.00000 0.00000 0.020
## [8,] 0.50624633 4.722717 0.00000 0.00000 0.014
## [9,] 1.31016373 9.364072 0.00000 18.84844 0.032
## [10,] 0.22695955 2.513061 0.00000 0.00000 0.014
## [11,] -1.69432196 20.001543 0.00000 0.00000 0.028
## [12,] -0.25492222 3.585282 0.00000 0.00000 0.012
## [13,] -0.73466078 6.461440 0.00000 0.00000 0.022
## [14,] -1.83830178 10.559279 -43.33420 0.00000 0.038
## [15,] 0.03930663 6.537587 0.00000 0.00000 0.022
## [16,] 0.18015253 2.319517 0.00000 0.00000 0.014
## [17,] 0.03130824 1.361797 0.00000 0.00000 0.012
## [18,] -1.87807674 10.840157 -40.52837 0.00000 0.036
## [19,] -0.15310310 3.071736 0.00000 0.00000 0.014
## [20,] 0.08208676 1.379057 0.00000 0.00000 0.006
## [21,] 0.17156932 3.733147 0.00000 0.00000 0.012plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -1.2529045 10.730147 -31.330506 18.380557 0.258
## [2,] -13.0881671 28.085738 -93.068549 12.242981 0.394
## [3,] -4.9825663 18.016028 -55.476330 20.865449 0.352
## [4,] 0.9588258 10.849730 -22.423150 30.141911 0.270
## [5,] -2.9542788 14.416081 -51.271414 17.225799 0.290
## [6,] 3.0709359 12.660109 -14.441693 37.265962 0.292
## [7,] 2.7376292 13.300219 -22.675584 38.331700 0.284
## [8,] 2.2880182 13.522575 -20.563550 35.574735 0.290
## [9,] 7.0934095 21.575502 -18.610142 73.395204 0.350
## [10,] 8.2643408 19.434287 -5.064555 69.564690 0.324
## [11,] -6.8637718 29.581977 -88.218785 30.909406 0.370
## [12,] -6.7185881 18.674257 -61.136654 16.151969 0.370
## [13,] -7.0997808 19.273637 -66.539792 15.104492 0.336
## [14,] -13.2076165 25.579187 -89.779409 7.673275 0.420
## [15,] 6.9815853 18.030428 -6.311038 64.075998 0.306
## [16,] 3.0213070 12.731469 -14.934310 45.493061 0.250
## [17,] 0.8139605 13.690379 -25.523666 32.665027 0.300
## [18,] -17.6271428 28.414522 -94.024979 2.988976 0.482
## [19,] -1.3052406 9.930916 -30.761027 16.085328 0.246
## [20,] 1.0247298 11.138782 -20.880505 28.447281 0.264
## [21,] 0.2244173 12.085502 -26.647282 26.043596 0.244plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
3.2 Run the NPB model with temperaure and ozone
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4c.2.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4c.2.rdata"))
npb.sum2 <- summary(fit.npb2)3.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -15.0400987 28.63075 -94.306370 13.071278 0.4520
## mean_o3 -15.4764202 31.29159 -103.482537 11.847902 0.4292
## mean_temp 0.8637020 17.33207 -36.221436 43.815375 0.3156
## pct_tree_cover 1.1703175 10.61831 -19.920745 31.349966 0.2704
## pct_impervious -0.9943910 10.01024 -29.385274 19.572781 0.2476
## mean_aadt_intensity 3.3078308 11.53627 -10.500466 38.221276 0.2780
## dist_m_tri 3.5042320 13.59236 -15.322403 43.897194 0.2984
## dist_m_npl 0.8927001 15.46597 -28.775335 31.998629 0.2868
## dist_m_waste_site 8.4303467 19.94186 -9.894573 65.388107 0.3760
## dist_m_major_emit 7.7876799 18.99636 -8.721286 63.218522 0.3488
## dist_m_cafo -5.3754130 30.34930 -83.783903 36.032849 0.3592
## dist_m_mine_well -0.3763322 13.37283 -33.871019 28.713684 0.2888
## cvd_rate_adj -2.4834185 15.79817 -47.777595 27.253051 0.3160
## res_rate_adj -16.3563994 28.97361 -93.578118 6.286628 0.4468
## violent_crime_rate 4.4861756 14.57330 -10.361279 48.603636 0.2984
## property_crime_rate 1.8534708 10.95868 -15.054892 31.426820 0.2596
## pct_less_hs 1.4767809 13.55808 -22.218749 36.400179 0.2752
## pct_unemp -12.2979023 23.95060 -80.167506 7.271875 0.4056
## pct_limited_eng -2.2029122 12.87752 -39.750439 19.373807 0.2668
## pct_hh_pov 1.3132853 12.23588 -21.524834 34.543378 0.2632
## pct_poc 1.6494979 12.60715 -19.403174 35.466016 0.28243.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum2$covariates)[2:nrow(npb.sum2$covariates)] <- colnames(W.scaled2)
npb.sum2$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 2968.897683 240.18110 2493.374742 3438.71608
## lat -5.480747 350.72021 -694.947932 699.52599
## lon -42.919075 164.09292 -370.323972 270.22948
## lat_lon_int -22.758268 416.03869 -830.350149 807.06481
## ed_no_hs 268.665566 117.65024 40.687316 506.40831
## ed_hs 256.676773 111.47898 40.249877 474.91021
## ed_aa 127.321375 105.96958 -73.632993 337.59438
## ed_4yr 179.977486 112.49492 -42.009683 409.21912
## low_bmi 29.719605 126.18006 -225.282326 276.28198
## ovwt_bmi 97.276471 55.25937 -10.404890 203.34379
## obese_bmi 148.568817 58.80074 33.117813 260.77065
## concep_spring -111.305866 72.65737 -252.596530 29.73691
## concep_summer -16.627547 95.69096 -227.998382 154.72735
## concep_fall 15.578349 82.62738 -155.647270 164.30867
## concep_2010 -80.117243 236.81352 -553.762565 380.01833
## concep_2011 -96.492246 226.90871 -535.720509 335.19240
## concep_2012 63.781660 228.25065 -387.005053 510.28847
## concep_2013 105.167354 226.19673 -334.010986 539.68052
## maternal_age 48.835601 27.95352 -5.579823 104.35857
## any_smoker -179.018227 79.28374 -338.438182 -28.46686
## smokeSH -75.661193 53.93359 -182.548767 31.01679
## mean_cpss -1.480142 27.59347 -55.758928 50.28400
## mean_epsd -55.572975 27.31268 -107.918628 -1.19997
## male 235.582807 44.66175 147.274566 321.592553.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum2$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 28.1887482288 49.05514274 0.000000 148.2339 0.2744
## [2,] 1.3131081276 10.35393346 0.000000 0.0000 0.0232
## [3,] -0.0917138713 1.53858175 0.000000 0.0000 0.0060
## [4,] -0.0131010052 0.88838275 0.000000 0.0000 0.0040
## [5,] 0.0736029976 2.15373437 0.000000 0.0000 0.0068
## [6,] -0.0448202473 0.94827597 0.000000 0.0000 0.0040
## [7,] -0.0285005244 1.38220859 0.000000 0.0000 0.0064
## [8,] -0.1261093762 1.79679962 0.000000 0.0000 0.0076
## [9,] -0.1319406190 2.04625050 0.000000 0.0000 0.0072
## [10,] -0.0445847595 0.86241997 0.000000 0.0000 0.0032
## [11,] -0.0530454799 1.27574895 0.000000 0.0000 0.0056
## [12,] -0.0441589444 1.05319037 0.000000 0.0000 0.0044
## [13,] -0.0058957564 0.88336896 0.000000 0.0000 0.0036
## [14,] 0.0115685346 0.99151068 0.000000 0.0000 0.0032
## [15,] 0.0982782784 2.45416369 0.000000 0.0000 0.0044
## [16,] -0.0681654966 1.24884636 0.000000 0.0000 0.0040
## [17,] -0.0139580496 0.80125927 0.000000 0.0000 0.0028
## [18,] -0.1964555561 2.56385226 0.000000 0.0000 0.0084
## [19,] -0.0481477094 0.96573055 0.000000 0.0000 0.0052
## [20,] -0.0240713517 0.73848372 0.000000 0.0000 0.0028
## [21,] -206.2125821425 26.20824599 -258.268490 -156.1275 1.0000
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## [585,] -0.0646800360 1.43685882 0.000000 0.0000 0.0056
## [586,] -0.0462468819 5.72460017 0.000000 0.0000 0.0076
## [587,] 0.0310824768 1.45195070 0.000000 0.0000 0.0020
## [588,] 0.2625842175 4.88583723 0.000000 0.0000 0.0076
## [589,] -0.0600922962 1.57369833 0.000000 0.0000 0.0048
## [590,] 0.0085786886 3.59896153 0.000000 0.0000 0.0080
## [591,] -0.1476379811 3.92266498 0.000000 0.0000 0.0060
## [592,] 0.0821139875 3.49696612 0.000000 0.0000 0.0068
## [593,] -0.1020889230 2.27530753 0.000000 0.0000 0.0064
## [594,] 0.0428747086 2.14784732 0.000000 0.0000 0.0052
## [595,] -0.1047010156 6.49800137 0.000000 0.0000 0.0080
## [596,] -0.0432069578 0.96983860 0.000000 0.0000 0.0032
## [597,] 0.1575885874 4.45612680 0.000000 0.0000 0.0052
## [598,] 0.4815410140 6.84389507 0.000000 0.0000 0.0072
## [599,] -0.0233258251 1.17038753 0.000000 0.0000 0.0060
## [600,] 0.0610965138 1.90413243 0.000000 0.0000 0.0040
## [601,] 0.0421500137 2.12151170 0.000000 0.0000 0.0048
## [602,] 0.0500769320 2.17830926 0.000000 0.0000 0.0048
## [603,] -0.1675848490 2.42688825 0.000000 0.0000 0.0084
## [604,] -0.0379813336 1.03049234 0.000000 0.0000 0.0048
## [605,] -0.0593494680 2.76244824 0.000000 0.0000 0.0064
## [606,] -0.0108868982 1.30784658 0.000000 0.0000 0.0048
## [607,] -0.1139151105 2.35880065 0.000000 0.0000 0.0060
## [608,] -0.0263281383 1.20242967 0.000000 0.0000 0.0056
## [609,] -0.2614575429 7.39902488 0.000000 0.0000 0.0064
## [610,] -0.3503280808 6.13296607 0.000000 0.0000 0.0068
## [611,] 0.1173816024 3.68735802 0.000000 0.0000 0.0048
## [612,] -0.2424616581 4.59740137 0.000000 0.0000 0.0076
## [613,] 0.0444051720 3.01405177 0.000000 0.0000 0.0056
## [614,] -1.4777863482 15.47448634 0.000000 0.0000 0.0156
## [615,] -0.0302196290 1.42166587 0.000000 0.0000 0.0044
## [616,] -0.1564661194 4.99367869 0.000000 0.0000 0.0092
## [617,] -0.1608200267 4.29557640 0.000000 0.0000 0.0064
## [618,] 0.0491568295 2.59896675 0.000000 0.0000 0.0028
## [619,] -0.0196546874 1.47712036 0.000000 0.0000 0.0044
## [620,] -0.3626987193 8.74035295 0.000000 0.0000 0.0080
## [621,] -0.8790074235 10.83180971 0.000000 0.0000 0.0104
## [622,] -0.0672634759 1.56165971 0.000000 0.0000 0.0056
## [623,] -0.0141782621 1.08791902 0.000000 0.0000 0.0048
## [624,] -0.1839401771 3.22835543 0.000000 0.0000 0.0076
## [625,] -0.1580815176 2.80378448 0.000000 0.0000 0.0080
## [626,] -0.2257300669 3.86171148 0.000000 0.0000 0.0068
## [627,] -0.0355392306 1.27124146 0.000000 0.0000 0.0024
## [628,] 0.0120803067 2.15798267 0.000000 0.0000 0.0036
## [629,] -0.0828119175 2.73008678 0.000000 0.0000 0.0056
## [630,] -0.0267016713 1.71251306 0.000000 0.0000 0.0060
## [631,] -0.0592281892 5.20616797 0.000000 0.0000 0.0064
## [632,] -0.5885150720 9.05423577 0.000000 0.0000 0.0128
## [633,] -0.0305801989 0.89603945 0.000000 0.0000 0.0024
## [634,] 0.2387725098 4.70764664 0.000000 0.0000 0.0080
## [635,] -0.1627806885 4.49210520 0.000000 0.0000 0.0044
## [636,] -0.0617112089 2.54637993 0.000000 0.0000 0.0052
## [637,] 0.0350711713 3.58469728 0.000000 0.0000 0.0044
## [638,] 0.2095100629 4.11866991 0.000000 0.0000 0.0052
## [639,] -0.0342798600 1.33261491 0.000000 0.0000 0.0024
## [640,] -0.0084099888 0.84954552 0.000000 0.0000 0.0028
## [641,] -0.1385948444 3.87861364 0.000000 0.0000 0.0060
## [642,] 0.0293340062 0.81526387 0.000000 0.0000 0.0028
## [643,] -0.6685166101 11.61380435 0.000000 0.0000 0.0072
## [644,] -0.0682290560 1.75600204 0.000000 0.0000 0.0052
## [645,] 0.0092579167 1.80028140 0.000000 0.0000 0.0048
## [646,] -0.0273464221 0.92217265 0.000000 0.0000 0.0036
## [647,] -0.0854202641 2.43718698 0.000000 0.0000 0.0060
## [648,] 0.0459801096 2.31289800 0.000000 0.0000 0.0032
## [649,] -0.1096894450 1.39330213 0.000000 0.0000 0.0084
## [650,] -0.2417299673 3.27174611 0.000000 0.0000 0.0080
## [651,] 0.2042338004 4.44568737 0.000000 0.0000 0.0056
## [652,] -0.1766229152 2.66261031 0.000000 0.0000 0.0076
## [653,] 0.0134780550 2.23058113 0.000000 0.0000 0.0036
## [654,] 0.1556819609 5.13217222 0.000000 0.0000 0.0072
## [655,] -0.3363839413 8.77449805 0.000000 0.0000 0.0100
## [656,] -0.0685256950 1.87948726 0.000000 0.0000 0.0072
## [657,] 0.0717129330 2.91825108 0.000000 0.0000 0.0068
## [658,] -0.0721913257 1.66795064 0.000000 0.0000 0.0036
## [659,] -0.0192637629 2.90982126 0.000000 0.0000 0.0044
## [660,] -0.0902501130 2.35798575 0.000000 0.0000 0.0040
## [661,] 0.0024061770 2.38168227 0.000000 0.0000 0.0040
## [662,] 0.0193289832 2.71049490 0.000000 0.0000 0.0064
## [663,] 0.2552594658 4.96866040 0.000000 0.0000 0.0060
## [664,] -0.0359991062 1.08722342 0.000000 0.0000 0.0040
## [665,] -0.0044164597 0.78245187 0.000000 0.0000 0.0044
## [666,] -0.3611609014 7.92386045 0.000000 0.0000 0.0080
## [667,] 0.0073752164 1.37813136 0.000000 0.0000 0.0052
## [668,] -0.0385130085 0.81978164 0.000000 0.0000 0.0040
## [669,] -0.0551265379 1.54411194 0.000000 0.0000 0.0040
## [670,] -0.0557528777 1.85029759 0.000000 0.0000 0.0048
## [671,] 0.0907486359 2.10358646 0.000000 0.0000 0.0040
## [672,] -0.1615316574 2.54481808 0.000000 0.0000 0.0084
## [673,] -0.0858680825 1.35458873 0.000000 0.0000 0.0076
## [674,] -0.0525483042 1.83533256 0.000000 0.0000 0.0052
## [675,] -0.1448204010 2.79079210 0.000000 0.0000 0.0076
## [676,] -0.0371730028 1.37144680 0.000000 0.0000 0.0052
## [677,] 0.0950271444 3.51175568 0.000000 0.0000 0.0056
## [678,] 0.0034452835 5.18832726 0.000000 0.0000 0.0060
## [679,] 0.1106510096 3.18050479 0.000000 0.0000 0.0028
## [680,] 0.0668577817 1.94929540 0.000000 0.0000 0.0048
## [681,] -0.0329033077 0.91556795 0.000000 0.0000 0.0036
## [682,] 0.0199787182 2.48599485 0.000000 0.0000 0.0068
## [683,] -0.0581867326 3.29939382 0.000000 0.0000 0.0084
## [684,] 0.0852966000 3.23355938 0.000000 0.0000 0.0084
## [685,] -0.1779685780 3.67182750 0.000000 0.0000 0.0068
## [686,] 0.1297996562 3.45998648 0.000000 0.0000 0.0044
## [687,] -0.1007538099 1.67679173 0.000000 0.0000 0.0056
## [688,] -0.0402634947 0.93569888 0.000000 0.0000 0.0040
## [689,] 0.0513569057 2.47398340 0.000000 0.0000 0.0040
## [690,] -0.0045080349 1.36656737 0.000000 0.0000 0.0028
## [691,] -0.1401440689 2.30575600 0.000000 0.0000 0.0052
## [692,] -0.0527173460 1.37532287 0.000000 0.0000 0.0032
## [693,] 0.1029519464 3.11296613 0.000000 0.0000 0.00443.2.4 Predict fitted values for each individual
pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals3.2.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")
4 Linear models for each predictor
4.1 Screening the exposures
Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 3.14 ppb
lm_results <- data.frame()
for(i in 1:length(colnames(X.scaled))) {
lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
names(lm_df)[2] <- colnames(X.scaled)[i]
ad_lm <- lm(birth_weight ~ ., data = lm_df)
temp <- data.frame(exp = colnames(X.scaled)[i],
beta = summary(ad_lm)$coefficients[2,1],
beta.se = summary(ad_lm)$coefficients[2,2],
p.value = summary(ad_lm)$coefficients[2,4])
temp$lcl <- temp$beta - 1.96*temp$beta.se
temp$ucl <- temp$beta + 1.96*temp$beta.se
lm_results <- bind_rows(lm_results, temp)
rm(temp)
}
lm_resultswrite_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4c.csv"))5 Linear model with the ozone and temperature predictors
The mean and standard deviation of the mean_o3 variable are 48.11 (3.14) ppb The mean and standard deviation of the mean_temp variable is 52.67 (4.69) degrees F
lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"#names(lm_df)[2] <- "mean_o3"
head(lm_df)bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = lm_df)
summary(bw_lm)##
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp +
## lat + lon + lat_lon_int + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1659.22 -309.97 29.09 320.30 1471.90
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2690.378 504.745 5.330 0.000000160 ***
## mean_o3 -202.202 84.710 -2.387 0.0174 *
## mean_temp 150.584 86.192 1.747 0.0813 .
## lat -3309.480 26030.095 -0.127 0.8989
## lon 1517.986 12042.902 0.126 0.8998
## lat_lon_int -3949.994 30989.410 -0.127 0.8986
## ed_no_hs 295.170 124.072 2.379 0.0178 *
## ed_hs 280.067 118.869 2.356 0.0189 *
## ed_aa 153.791 115.352 1.333 0.1832
## ed_4yr 218.451 122.524 1.783 0.0753 .
## low_bmi 21.427 128.666 0.167 0.8678
## ovwt_bmi 92.651 56.411 1.642 0.1012
## obese_bmi 146.402 59.992 2.440 0.0151 *
## concep_spring -206.239 84.598 -2.438 0.0152 *
## concep_summer -144.213 106.079 -1.359 0.1747
## concep_fall -41.944 99.462 -0.422 0.6735
## concep_2010 251.274 499.014 0.504 0.6148
## concep_2011 192.469 500.887 0.384 0.7010
## concep_2012 462.105 505.747 0.914 0.3614
## concep_2013 354.254 499.469 0.709 0.4786
## maternal_age 49.688 27.880 1.782 0.0754 .
## any_smoker -180.011 80.822 -2.227 0.0265 *
## smokeSH -64.233 54.844 -1.171 0.2422
## mean_cpss 8.848 27.373 0.323 0.7467
## mean_epsd -63.300 27.252 -2.323 0.0207 *
## male 234.295 46.608 5.027 0.000000736 ***
## mean_o3:mean_temp -203.061 23.211 -8.748 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 476 on 425 degrees of freedom
## Multiple R-squared: 0.2944, Adjusted R-squared: 0.2512
## F-statistic: 6.819 on 26 and 425 DF, p-value: < 0.00000000000000022plot(bw_lm)## Warning: not plotting observations with leverage one:
## 1
6 Try a GAM with the ozone and temperature predictor
The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone and temperature to see about potential nonlinear effects
The mean and standard deviation of the mean_o3 variable are 48.11 (3.14) ppb The mean and standard deviation of the mean_temp variable is 52.67 (4.69) degrees F
library(mgcv)## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## This is mgcv 1.8-34. For overview type 'help("mgcv-package")'.library(tidymv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"#names(gam_df)[2] <- "mean_o3"
head(gam_df)bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df, method = "REML")
gam.check(bw_gam)
##
## Method: REML Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-0.0007907339,0.00003581137]
## (score 3271.262 & scale 200669.8).
## Hessian positive definite, eigenvalue range [4.649398,213.2882].
## Model rank = 53 / 53
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(mean_o3,mean_temp) 29.0 17.5 0.99 0.41summary(bw_gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2458.848 487.458 5.044 0.000000685 ***
## lat -6230.541 25040.236 -0.249 0.8036
## lon 2862.928 11585.059 0.247 0.8049
## lat_lon_int -7427.282 29810.771 -0.249 0.8034
## ed_no_hs 229.723 120.368 1.909 0.0570 .
## ed_hs 200.488 115.295 1.739 0.0828 .
## ed_aa 115.944 111.300 1.042 0.2982
## ed_4yr 172.293 117.681 1.464 0.1439
## low_bmi 20.693 123.990 0.167 0.8675
## ovwt_bmi 79.593 54.308 1.466 0.1435
## obese_bmi 116.811 57.709 2.024 0.0436 *
## concep_spring -144.484 93.161 -1.551 0.1217
## concep_summer -148.931 133.987 -1.112 0.2670
## concep_fall -43.349 127.059 -0.341 0.7331
## concep_2010 398.744 487.663 0.818 0.4140
## concep_2011 265.985 490.420 0.542 0.5879
## concep_2012 634.187 494.055 1.284 0.2000
## concep_2013 467.863 488.748 0.957 0.3390
## maternal_age 54.643 26.682 2.048 0.0412 *
## any_smoker -199.583 77.274 -2.583 0.0101 *
## smokeSH -59.088 52.319 -1.129 0.2594
## mean_cpss 2.723 26.460 0.103 0.9181
## mean_epsd -51.200 26.062 -1.965 0.0501 .
## male 209.790 44.931 4.669 0.000004102 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 17.48 22.45 6.41 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.337 Deviance explained = 39.6%
## -REML = 3271.3 Scale est. = 2.0067e+05 n = 452save(gam_df, bw_gam, file = here::here("Results", "BW_GAM_v4c.rdata"))library(mgcViz)## Loading required package: qgam## Loading required package: rgl## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## Registered S3 method overwritten by 'mgcViz':
## method from
## +.gg GGally##
## Attaching package: 'mgcViz'## The following objects are masked from 'package:stats':
##
## qqline, qqnorm, qqplotgam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4c.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500) 7 GAM Sensitivity Analysis
The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.
Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.
library(mgcv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"head(gam_df)gam_df2 <- gam_df %>%
filter(mean_o3 > -2 & mean_o3 < 2) %>%
filter(mean_temp > -2 & mean_temp < 2)
hist(gam_df2$mean_o3)
hist(gam_df2$mean_temp)
bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df2, method = "REML")
gam.check(bw_gam2)
##
## Method: REML Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-0.002508048,0.00007001415]
## (score 3213.214 & scale 200352).
## Hessian positive definite, eigenvalue range [2.617209,209.6741].
## Model rank = 53 / 53
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(mean_o3,mean_temp) 29.0 13.9 0.98 0.33summary(bw_gam2)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2485.535 485.963 5.115 0.000000485 ***
## lat -8829.102 25156.449 -0.351 0.72579
## lon 4062.130 11638.673 0.349 0.72725
## lat_lon_int -10517.366 29949.212 -0.351 0.72564
## ed_no_hs 237.733 120.074 1.980 0.04839 *
## ed_hs 207.494 114.940 1.805 0.07178 .
## ed_aa 133.082 111.271 1.196 0.23238
## ed_4yr 172.180 117.485 1.466 0.14354
## low_bmi 11.100 123.853 0.090 0.92863
## ovwt_bmi 77.168 54.497 1.416 0.15754
## obese_bmi 113.451 58.194 1.950 0.05192 .
## concep_spring -135.713 92.510 -1.467 0.14315
## concep_summer -141.159 131.259 -1.075 0.28282
## concep_fall -45.434 124.243 -0.366 0.71479
## concep_2010 398.176 485.636 0.820 0.41275
## concep_2011 266.905 488.188 0.547 0.58487
## concep_2012 609.442 491.975 1.239 0.21615
## concep_2013 465.282 486.707 0.956 0.33965
## maternal_age 54.773 26.740 2.048 0.04117 *
## any_smoker -214.412 77.843 -2.754 0.00614 **
## smokeSH -62.748 52.606 -1.193 0.23365
## mean_cpss 1.939 26.609 0.073 0.94193
## mean_epsd -49.795 26.136 -1.905 0.05745 .
## male 201.636 45.062 4.475 0.000009948 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 13.92 18.67 3.13 0.0000164 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.235 Deviance explained = 29.8%
## -REML = 3213.2 Scale est. = 2.0035e+05 n = 445save(gam_df2, bw_gam2, file = here::here("Results", "BW_GAM_Sensitivity_v4c.rdata"))library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4c.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)